Many individuals carry drink containers that hold water or other hot or cold potable beverages. These drink containers typically include a vessel that is formed from plastic or metal. These containers also frequently include a closure, which is removably secured to a neck or other opening of the vessel. Some conventional drink containers further include a drink spout, or nozzle, that is integral with the closure and from which liquid may be drawn from the vessel without removal of the closure from the vessel. Some such nozzles include a manual or automatic valve for selectively restricting liquid from being dispensed through the drink spout, and some do not. For example, some such drink containers have a closure with a drink spout that may be selectively opened and closed to permit a user to selectively seal and unseal the drink spout, and some drink containers and/or closures further include a manual actuator for selectively opening and closing the drink spout. Examples of such drink containers with valved drink spouts include squeezable drink containers with rotating or push-pull drink spouts and CAMELBAK® brand drink containers with bite-actuated mouthpieces. When such containers are used with beverages other than water, such as that include sugar or other suspended particulates that may stick to or otherwise foul components associated with drink spouts, valves, or other components of the closure, it may be difficult to clean these portions of the closure. Thus, there exists a need for drink containers with improved closure assemblies.